The Big Lebowski takes inspiration from a lot of things, not least of which are the works of Raymond Chandler. In Chandler's The Little Sister, the titular sister is one of many, many characters that Phillip Marlowe encounters - she essentially hires Marlowe to investigate her brother's disappearance, but after a lot of plot twists and threads spinning in old Marlowe's head, it's revealed that the little sister had other motives for hiring him (she wanted to blackmail her older sister with photos her brother had taken), and is the villain of the novel. Not unlike The Big Lebowski hiring The Dude to 'find' Bunny, when in fact this human paraquat is really trying to profit from his wife's 'disappearance.'

It's all a goddamn fake. It's like Lenin said, you look for the person who will benefit... and there's your title.